Details

analyze2.0s (19.8%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
9.4%	90.4%	0.2%	9
9.4%	90.4%	0.2%	10
10.9%	88.9%	0.2%	11
10.9%	88.9%	0.2%	12
10.9%	88.9%	0.2%	13
10.9%	88.9%	0.2%	14

sample188.0ms (1.9%)

Algorithm

1×

intervals

Results

112.0ms	109×	body	1280	valid
40.0ms	74×	body	640	valid
13.0ms	36×	body	320	valid
4.0ms	17×	body	160	valid
2.0ms	20×	body	80	valid

simplify17.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	270	20
1	270	20

prune10.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.5b

Counts

2 → 1

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
2.8b	(sin (- lambda1 lambda2))
3.0b	(cos (- lambda1 lambda2))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-log-exp`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
3×	`cos-diff`
2×	`sub-neg` `associate-+r+`
1×	`+-commutative` `distribute-rgt-in` `cos-sum` `distribute-lft-in` `flip3-+` `sin-sum` `sum-log` `sin-diff` `flip-+`

Counts

4 → 38

Calls

4 calls:

4.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms	(cos (- lambda1 lambda2))
4.0ms	(sin (- lambda1 lambda2))
1.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))

series48.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

28.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
9.0ms	(atan2 (* (cos phi2) (sin (- lambda1 lambda2))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
5.0ms	(cos (- lambda1 lambda2))
5.0ms	(sin (- lambda1 lambda2))

simplify51.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4947	591
1	4947	591

prune147.0ms (1.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	40	10	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	41	10	51

Merged error: 0.3b

Counts

51 → 10

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))))
0.2b	(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
0.5b	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
3.0b	(cos (- lambda1 lambda2))

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `add-log-exp`
3×	`cos-diff` `sub-neg` `associate-r` `associate-l`
2×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `associate-*r/`
1×	`+-commutative` `cos-sum` `flip3--` `flip3-+` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `unswap-sqr`

Counts

4 → 51

Calls

4 calls:

7.0ms	(* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))))
4.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
4.0ms	(cos (- lambda1 lambda2))
1.0ms	(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))

series71.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

32.0ms	(* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))))
24.0ms	(+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2))))
10.0ms	(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (cos (- lambda1 lambda2)))))
4.0ms	(cos (- lambda1 lambda2))

simplify52.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5090	985

prune142.0ms (1.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	62	1	63
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	63	10	73

Merged error: 0.1b

Counts

73 → 10

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))))
0.2b	(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
0.2b	(* (sin lambda1) (sin lambda2))
0.5b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`associate-r` `associate-l` `add-log-exp`
2×	`distribute-rgt-in` `sub-neg` `associate-+r+` `distribute-lft-in` `associate-r/` `pow-prod-down` `prod-exp` `-commutative` `cbrt-unprod` `unswap-sqr`
1×	`+-commutative` `flip3--` `flip3-+` `sum-log` `flip--` `flip-+` `sin-mult`

Counts

4 → 61

Calls

4 calls:

9.0ms	(* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))))
5.0ms	(* (sin lambda1) (sin lambda2))
4.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
1.0ms	(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))

series107.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

51.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2)))))
33.0ms	(* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2))))
14.0ms	(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (* (sin lambda1) (sin lambda2))))))
9.0ms	(* (sin lambda1) (sin lambda2))

simplify47.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5159	1240

prune155.0ms (1.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	73	10	83

Merged error: 0.0b

Counts

83 → 10

localize35.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
0.2b	(* (sin lambda1) (sin lambda2))
0.5b	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))
3.7b	(log (exp (* (sin lambda1) (sin lambda2))))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
3×	`log-prod` `associate-r` `associate-l` `log-pow`
2×	`associate-+r+`
1×	`+-commutative` `distribute-rgt-in` `exp-prod` `exp-to-pow` `distribute-lft-in` `flip3-+` `rem-log-exp` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `sin-mult` `unswap-sqr`

Counts

4 → 53

Calls

4 calls:

5.0ms	(* (sin lambda1) (sin lambda2))
4.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))
2.0ms	(log (exp (* (sin lambda1) (sin lambda2))))
1.0ms	(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))

series87.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

54.0ms	(+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2)))))))
14.0ms	(atan2 (* (cos phi2) (- (* (cos lambda2) (sin lambda1)) (* (cos lambda1) (sin lambda2)))) (+ (cos phi1) (* (cos phi2) (+ (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin lambda2))))))))
10.0ms	(log (exp (* (sin lambda1) (sin lambda2))))
10.0ms	(* (sin lambda1) (sin lambda2))

simplify29.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5488	956

prune96.0ms (0.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	65	10	75

Merged error: 0.0b

Counts

75 → 10

regimes585.0ms (5.8%)

Accuracy

Total 0.1b remaining (49.7%)

Threshold costs 0.1b (49.7%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	58	36
1	58	36

end0.0ms (0%)

sample6.1s (60.4%)

Algorithm

1×

intervals

Results

3.9s	3616×	body	1280	valid
1.4s	2353×	body	640	valid
380.0ms	993×	body	320	valid
97.0ms	383×	body	160	valid
77.0ms	654×	body	80	valid
3.0ms	1×	body	2560	valid

Details

analyze2.0s (19.8%)

sample188.0ms (1.9%)

simplify17.0ms (0.2%)

prune10.0ms (0.1%)

localize21.0ms (0.2%)

rewrite13.0ms (0.1%)

series48.0ms (0.5%)

simplify51.0ms (0.5%)

prune147.0ms (1.5%)

localize30.0ms (0.3%)

rewrite16.0ms (0.2%)

series71.0ms (0.7%)

simplify52.0ms (0.5%)

prune142.0ms (1.4%)

localize29.0ms (0.3%)

rewrite20.0ms (0.2%)

series107.0ms (1.1%)

simplify47.0ms (0.5%)

prune155.0ms (1.5%)

localize35.0ms (0.3%)

rewrite13.0ms (0.1%)

series87.0ms (0.9%)

simplify29.0ms (0.3%)

prune96.0ms (0.9%)

regimes585.0ms (5.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample6.1s (60.4%)

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